Newly Developed Multiparameter Bulk Cloud Schemes. Part I: A New Triple-moment Condensation Scheme and Tests

Abstract Double-moment schemes cannot accurately describe the evolution of the cloud droplet spectrum during condensation. Hence, a new triple-moment condensation scheme is developed to describe the evolution of cloud droplet spectra. In this scheme, a three-parameter gamma distribution function of the cloud droplet mass is adopted, and the prognostic equations of the spectral shape parameter and slope parameter are derived by means of the number concentration, cloud water content and reflectivity factor of cloud droplets. The new parameterization scheme is compared with high-resolution Lagrangian and Eulerian bin schemes, double-moment schemes, and existing triple-moment schemes by performing simulations under different supersaturation values. The new scheme can reduce the cloud spectral error in the cloud water content and reflectivity factor caused by the fixed shape parameter in some bulk schemes. The spectra simulated with the new scheme match the Lagrangian analytical solutions well, with errors within approximately 1% in the cloud water content and reflectivity factor. The effects of curvature and solution on condensation growth are also tested using the new scheme, and a method of using multiple gamma distribution functions to characterize the multimodal spectrum of cloud droplets is proposed in the new condensation scheme. Ultimately, the formation of rain embryos from giant aerosols can be simulated via the new scheme.